Pulleys Pulleys Everywhere -3

Classical Mechanics Level 2

System is shown in the figure and man is pulling the rope form both sides with constant speed $u$ . Then the speed of the block will be? ( $M$ can only move vertically)

\frac{3u}{4}

\frac{3u}{2}

\frac{u}{4}

None of these choices

1 solution

Satvik Pandey
Apr 13, 2015

Imagine blocks A and B being pulled at the speed of $u$ instead of man pulling the string at speed $u$ .

By the concept of virtual-work method $\sum { \vec { T } .\vec { V } } =0$

Let the velocity of mass $M$ be $v$ in upward direction. Applying "T.V" we get

$-Tu-\frac{Tu}{2}+2Tv=0$

So $v=\frac{3u}{4}$ .

Another method would be equating the pulling causes and the releasing causes.

Ronak Agarwal - 6 years, 2 months ago

Yes but I think this is easier. :)

satvik pandey - 6 years, 2 months ago

My method is much easier since one can orally solve such problems.

Ronak Agarwal - 6 years, 2 months ago

@Ronak Agarwal – Can you post your solution. I would like to learn your's method too. :)

satvik pandey - 6 years, 2 months ago

@Satvik Pandey – I am on mobile hence it would be tough for me to post solution , but I will try to explain in this comment.

Pick one whole string, there are total of two independent string. Pick the long one.

Pulling causes.

The man pulling the string on the right =u The pulley on the left just above the small fixed support = 2u ( pulley moves with speed u pulling string from both sides)

Net pull=3u

Releasing causes

The mass M moving =4v(v is the speed of the mass, observe carefully it is releasing string by 4 point)

Net release=4v

Equate the pull and the release , you can try this method on other constraint finding problems it is seriously effective.

Ronak Agarwal - 6 years, 2 months ago

@Ronak Agarwal – I got that! Thank you for sharing your method. :)

Could you please suggest some Maths books here ?

satvik pandey - 6 years, 2 months ago

@Ronak Agarwal – Wao. ! That's a very helpful method :) thanks

Prashant Kr - 6 years, 1 month ago

But in sign convention how have you taken both upper one negative

Sarita Patel - 2 years, 11 months ago

That is confusing me too.

Vidhi Patidar - 1 year, 11 months ago

Pulleys Pulleys Everywhere -3

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